Damage evolution in particulate composite materials
K. Matous
Department of Mechanical Aerospace & Nuclear
Engineering
Rensselaer Polytechnic Institute
110 8th Street, Troy, NY 12180
Abstract
Damage evolution in heterogeneous solids is modeled using
transformation field analysis and imperfect interface
model. Stress changes caused by local debonding are
simulated by residual stresses generated by equivalent
transformation strains or eigenstrains. Decohesion and
both overall and local stress and strain rates are derived
from thermodynamics of irreversible processes, which
provide excellent framework for the development of
constitutive equations. Both tangent and unloading secant
stiffness tensors are found along any prescribed
mechanical loading path. Numerical simulation of debonding
evolution in glass/elastomer composites is compared with
experimental data and provides good agreement between the
model and experiments.
Conclusion
The proposed mathematical model based on Dvorak's
transformation field analysis together with thermodynamics
of irreversible processes and the internal state variables
theory, which induces sufficient constraints against a set
of possibilities that is too large, is shown to describe
successfully the damage evolution in particularly
reinforced elastomers. Stress changes caused by local
debonding are simulated by residual stresses generated by
equivalent transformation strains or eigenstrains, which
are derived from Hashin's imperfect interface spring-layer
model. The energy release rate is derived from the free
energy function, and both the total and incremental
strain-based formulations including loading tangent and
unloading secant stiffness tensors are found for any
loading path. The current numerical approach is limited to
small deformations; however, good agreement between the
model and experiments for the uniaxial tension test
performed by Vratsanos and Farris was obtained for several
densities of reinforcement. The material completely
raptures before decohesion of all particles, especially
for high reinforcement densities and thus much stiffer and
brittle material. However, for low densities almost all
particles debond before rupture, so that the material
becomes porous and the fracture is very similar to
ductile. Based on such observations, the material
constraint condition for the percolation threshold of a
closely packed reinforcement is proposed and limits the
total decohesion. Further study is required to extend the
model to cover the nonlinear deformation of matrix.
Moreover, implementation of theory into a finite element
code is necessary for the solution of complex geometry
and/or boundary and loading conditions.
Acknowledgment
I wish to thank Professor G.J. Dvorak for helpful
discussions.